Leon,
You are getting too far ahead of me! Now I have to catch up.
Interesting that your scrapbook clipping of the "1931 TT" bike has no sump (forget the loop frame for a moment) so I'm not even sure if no sump rules out works bike.
Well HY2863 is captioned as a Junior machine, so as a 350cc could be an entirely different kettle of fish. I think that same variant, with a loop frame, was also used as a Douglas ISDT entrant along with more conventional models. And yet you have HY2878 also as a Junior entrant, in a duplex frame and using the 1930-32 sumps like the Senior mounts. A variety of different frames to attach the Junior entry list, different years (both have tartan tanks, so 1931 or later), or maybe the caption on HY2863 is in error and it was mistakenly identified as Junior entrant/contender.
I do not know the history of the I.o.M. TT in depth, so will have to defer to others about who did or did not race in a given year. I just know the highlights as related in books like "The Best Twin". Nor do I have (unfortunately) any of the Keig albums.
The reason I went for "1932" for the Bejarano bike is that the frame with the long steering head was supposedly new for the 1932 TT:
I have read that too, but I think the 1930-31 models started a trend towards a taller head stock. Of course, now I will have to look to see if I can find any pictures to back that up. The scarcity of images or survivors of a reliable provenance make it difficult.
The Works bike Henry Body has was I though supposed to be a 1930 frame and it has a tall head stock. Yet I am not so sure now as it does have 1932 engine, or at least set of heads. The frame might be '32, '31, and the whole thing could be a mix of years. It does appear to have been built after the change to Sturmey-Archer gearbox as it has the accommodation for a brake drum on the left, not right. But I have reason to believe the frame is not '32 (more anon).
This bike is supposed to be a 1930 Work model. Rear brake drum on the right to suit the cross-over Douglas transmission. The bike was sold to Japan years ago.

There seems to be a bit more gap between the upper and lower head stock lugs the normal, but perhaps that is just an illusion. Built up more at the top too, I think. Though maybe not as tall as the '32 model.
Next we have a picture of what is supposed to be Jack Douglas' Works sidecar bike prior to restoration. It had the transmission from a 1934-35 OW/OW1 road model fitted (poor choice!) but the frame was built for the chain line to be on the left, so would have had the Sturmey-Archer gearbox originally. I think this was supposed to be a 1931 entrant.

And here after restoration. Though note not the same petrol tank as the previous picture.

Then we have the late Bob Jones' sprinter that is supposedly based on a 1932 Work frame. Or so he told me.

With one of the unique feature identifying it as a '32 being the special lower rear lug to have a cross over brake shaft.

Presumably passing the shaft through the lower frame tube was out, as that was needed for the sidecar mounting. It also has the high foot rest mounting position seen on the Works bikes. But there are problems. The frame has the provision for the brake drum on the right. If it was a 1932 frame, it would have had a Sturmey-Archer gearbox, chain line on the left, and no need for a brake drum on the right. Unless they wanted to separate the brake drum and the sprocket for some reason. The bike as shown is set up for a sprocket/brake drum on the right (it is an earlier, and rare, 1926-28 I.o.M./TT brake drum), but the anchorage appears to be an addition rather than using the Douglas axle lug with the built-in brake anchorage. The other problem is the use of the DT type transmission platform. All the other 1930-32 Works have the platform projecting straight forward, rather than sweeping down. So I have my doubts. Unfortunately I did not have the presence of mind twenty-three years ago to look for a frame number when I took the photos.

It does have a tall head stock, but it is possible this and the other features are well engineered modification to a DT frame done long ago and having over time acquired the story (and a pannier petrol tank) of being a Works frame.
-Doug